The present invention relates to power-flow/voltage control in utility/industrial power networks of the types including many power plants/generators interconnected through transmission/distribution lines to other loads and motors. Each of these components of the power network is protected against unhealthy or alternatively faulty, over/under voltage, and/or over loaded damaging operating conditions. Such a protection is automatic and operates without the consent of power network operator, and takes an unhealthy component out of service by disconnecting it from the network. The time domain of operation of the protection is of the order of milliseconds.
The purpose of a utility/industrial power network is to meet the electricity demands of its various consumers 24-hours a day, 7-days a week while maintaining the quality of electricity supply. The quality of electricity supply means the consumer demands be met at specified voltage and frequency levels without over loaded, under/over voltage operation of any of the power network components. The operation of a power network is different at different times due to changing consumer demands and development or any faulty/contingency situation. In other words healthy operating power network is constantly subjected to small and large disturbances. These disturbances could be consumer/operator initiated, or initiated by overload and under/over voltage alleviating functions collectively referred to as security control functions and various optimization functions such as economic operation and minimization of losses, or caused by a fault/contingency incident.
For example, a power network is operating healthy and meeting quality electricity needs of its consumers. A fault occurs on a line or a transformer or a generator which faulty component gets isolated from the rest of the healthy network by virtue of the automatic operation of its protection. Such a disturbance would cause a change in the pattern of power flows in the network, which can cause over loading of one or more of the other components and/or over/under voltage at one or more nodes in the rest of the network. This in turn can isolate one or more other components out of service by virtue of the operation of associated protection, which disturbance can trigger chain reaction disintegrating the power network.
Therefore, the most basic and integral part of all other functions including optimizations in power network operation and control is security control. Security control means controlling power flows so that no component of the network in over loaded and controlling voltages such that there is no over voltage or under voltage at any of the nodes in the network following a disturbance small or large. As is well known, controlling electric power flows include both controlling real power flows which is given in MWs, and controlling reactive power flows which is given in MVARS. Security control functions or alternatively overloads alleviation and over/under voltage alleviation functions can be realized through one or combination of more controls in the network. These involve control of power flow over tie line connecting other utility network, turbine steam/water/gas input control to control real power generated by each generator, load shedding function curtails load demands of consumers, excitation controls reactive power generated by individual generator which essentially controls generator terminal voltage, transformer taps control connected node voltage, switching in/out in capacitor/reactor banks controls reactive power at the connected node.
Control of an electrical power system involving power-flow control and voltage control commonly is performed according to a process shown in FIG. 7, which is a method of forming/defining and solving a loadflow computation model of a power network to affect control of voltages and power flows in a power system comprising the steps of:    Step-10: obtaining on-line/simulated data of open/close status of all switches and circuit breakers in the power network, and reading data of operating limits of components of the power network including maximum Voltage X Ampere (VA or MVA) limits of transmission lines and transformers; and PV-node, a generator-node where Real-Power-P and Voltage-Magnitude-V are given/assigned/specified/set, maximum and minimum reactive power generation capability limits of generators, and transformers tap position limits, or stated alternatively in a single statement as reading operating limits of components of the power network,    Step-20: obtaining on-line readings of given/assigned/specified/set Real-Power-P and Reactive-Power-Q at PQ-nodes, Real-Power-P and voltage-magnitude-V at PV-nodes, voltage magnitude and angle at a reference/slack node, and transformer turns ratios, wherein said on-line readings are the controlled variables/parameters,    Step-30: performing loadflow computation to calculate, depending on loadflow computation model used, complex voltages or their real and imaginary components or voltage magnitudes or their corrections and voltage angles or their corrections at nodes of the power network providing for calculation of power flow through different components of the power network, and to calculate reactive power generation and transformer tap-position indications,    Step-40: evaluating the results of Loadflow computation of step-30 for any over loaded power network components like transmission lines and transformers, and over/under voltages at different nodes in the power system,    Step-50: if the system state is acceptable implying no over loaded transmission lines and transformers and no over/under voltages, the process branches to step-70, and if otherwise. then to step-60,    Step-60: correcting one or more controlled variables/parameters set in step-20 or at later set by the previous process cycle step-60 and returns to step-30,    Step-70: affecting a change in power flow through components of the power network and voltage magnitudes and angles at the nodes of the power network by actually implementing the finally obtained values of controlled variables/parameters after evaluating step finds a good power system or stated alternatively as the power network without any overloaded components and under/over voltages, which finally obtained controlled variables/parameter however are stored for acting upon fast in case a simulated event actually occurs or stated alternatively as actually implementing the corrected controlled variables/parameters to obtain secure/correct/acceptable operation of power system.
Overload and under/over voltage alleviation functions produce changes in controlled variables/parameters in step-60 of FIG. 7. In other words controlled variables/parameters are assigned or changed to the new values in step-60. This correction in controlled variables/parameters could be even optimized in case of simulation of all possible imaginable disturbances including outage of a line and loss of generation for corrective action stored and made readily available for acting upon in case the simulated disturbance actually occurs in the power network. In fact simulation of all possible imaginable disturbances is the modern practice because corrective actions need be taken before the operation of individual protection of the power network components.
It is obvious that loadflow computation consequently is performed many times in real-time operation and control environment and, therefore, efficient and high-speed loadflow computation is necessary to provide corrective control in the changing power system conditions including an outage or failure of any of the power network components. Moreover, the loadflow computation must be highly reliable to yield converged solution under a wide range of system operating conditions and network parameters. Failure to yield converged loadflow solution creates blind spot as to what exactly could be happening in the network leading to potentially damaging operational and control decisions/actions in capital-intensive power utilities.
The power system control process shown in FIG. 7 is very general and elaborate. IL includes control of power-flows through network components and voltage control at network nodes. However, the control of voltage magnitude at connected nodes within reactive power generation capabilities of electrical machines including generators, synchronous motors, and capacitor/inductor banks, and within operating ranges of transformer taps is normally integral part of loadflow computation as described in “LTC Transformers and MVAR violations in the Fast Decoupled Load Flow, IEEE Trans., PAS-101, No. 9, PP. 3328-3332, September 1982.” If under/over voltage still exists in the results of loadflow computation, other control actions, manual or automatic, may be taken in step-60 in the above and in FIG. 7. For example, under voltage can be alleviated by shedding some of the load connected.
The prior art and present invention are described using the following symbols and terms:    Ypq=Gpq+jBpq: (p-q)th element or nodal admittance matrix without shunts    Ypp=Gpp+jBpp: p-th diagonal element of nodal admittance matrix without shunts    yp=gp+jbp: total shunt admittance at any node-p    Vp=ep+jfp=Vp∠θp: complex voltage of any node-p    Pp+jQp: net nodal injected power    RPp+jRQp: modified net nodal power injection specified    φp: rotation or transformation angle    [RP]: vector of modified real power injections at power-network nodes    [RQ]: vector of modified reactive power injections at power-network nodes    m: number of PQ-nodes    k: number of PV-nodes    n=m+k+1: total number of nodes    q>p: q is the node adjacent to node-p excluding the case of q=p    [ ]: indicates enclosed variable symbol to be a vector or a matrix    PQ-node: load-node, where, Real-Power-P and Reactive-Power-Q are specified    PV-node: generator-node, where, Real-Power-P and Voltage-Magnitude-V are specified    Loadflow Computation: Each node in a power network is associated with four electrical quantities, which are voltage magnitude, voltage angle, real power, and reactive power. The loadflow computation involves calculation/determination of two unknown electrical quantities for other two given/specified/scheduled/set/unknown electrical quantities for each node. In other words the loadflow computation involves determination of unknown quantities in dependence on the given/specified/scheduled/set/known electrical quantities.    Loadflow Model: a set of equations describing the physical power network and its operation for the purpose of loadflow computation. The term ‘loadflow model’ can be alternatively referred to as ‘model of the power network for loadflow computation’. The process of writing Mathematical equations that describe physical power network and its operation is called Mathematical Modeling. If the equations do not describe/represent the power network and its operation accurately the model is inaccurate, and the iterative loadflow computation method could be slow and unreliable in yielding converged loadflow computation. There could be variety of Loadflow Models depending on organization of set of equations describing the physical power network and its operation, including Newton Raphson Loadflow (NRL) Model, and Supert Super Decoupled Loadflow (SSDL) Model.
Loadflow Method: sequence of steps used to solve a set of equations describing the physical power network and its operation for the purpose of loadflow computation is called Loadflow Method, which term can alternatively be referred to as ‘loadflow computation method’ or ‘method of loadflow computation’. One word for a set of equations describing the physical power network and its operation is: Model. In other words, sequence of step used to solve a Loadflow Model is a Loadflow Method. The loadflow method involves definition/formation of a loadflow model and its solution. There could be variety of Loadflow Methods depending on a loadflow model and iterative scheme used to solve the model including Newton Raphson Loadflow (NRL) Methods, Supert Super Decoupled Loadflow (SSDL) Method.
Artificial Neural Network
Neural Network (NN) based prior art loadflow methods of the kind carried out as step-30 in FIG. 7 are described in “Stochastic Load Flow Analysis Using Artificial Neural Networks, 2006 IEEE” by A. Jain. S. C. Tripathy. R. Balasubramanian, and Y. Kawazoe; “Radial basis function neural network for power system load-flow, Electrical Power and Energy Systems 30 (2008) 60-66” by A. Karami and M. S. Mohammadi, and “Artificial neural networks for load flow and external equivalents studies, Electric Power Systems Research (2010) article in press” by H. H. Muller, M. J. Rider and C. A. Castro. In the above publications and others, various type of Artificial Neural Networks (ANNs) involved in loadflow computation are Multilayer Perceptron (MLP). Radial Basis Function (RBF), Counter Propagation (CP) and Hopefield model. Detailed description of various ANNs and their training and testing and validation process is available in “Principles of Neurocomputing for Science and Engineering, McGraw-Hill (2001)” by Fredric M. Ham and Ivica Kostanic, and Principles of Artificial Neural Networks, World Scientific Publication (2007)” by Daniel Graupe. Testing and validation of a trained ANN is to check if the trained ANN has learned to give accurate enough output data set/vector for a given input data set/vector, which was not used in the training process. It is intended to keep basic description of Artificial Neural Network and its training process short except inventive parts.
ANN is considered as an important technique of artificial intelligence. In recent years, ANNs have gained wide spread attention and they are being used successfully in many areas of power systems. Since the first research paper “Artificial neural-net based dynamic security assessment for electric power systems, IEEE Trans. Power System 4 (1) (1989) 220-226” by D. J. Sobajic and Y. H. Pao published, increasing literature demonstrates the potential of ANN especially in applications that take advantage of the speed of ANNs for on-line calculations and their inherent capacity to overcome modeling complexity. ANN can model any nonlinear function of a device or a system described/expressed by a nonlinear equation or simultaneous nonlinear equations without knowledge of the actual model structure. ANNs can learn complex non-linear relationships among variables/parameters of nonlinear equations through a set of input/output examples, and can approximate nonlinear functional relationship among power system or in general any device or system variables/parameters of interest. An invention of artificial (not actual operational data statistics stored over long period of time like long term, short term, and daily load curves) generation of input and output data sets/vectors by different multiplication factors applied to operational variables/parameters of a power system described by simultaneous nonlinear loadflow equations comprising simulation of feasible and continuous nonlinear operating region of the power system for the purpose of training, testing and validating, forming/defining, and storing ANN computation model and then solving said stored ANN computation model using general purpose computing apparatus can also be extended in general to any device or system. It can be said that outputs of a conventional loadflow method like NRL or SSDL are functions of the operating conditions of a power system, and ANNs can be employed to approximate these functions. An attractive feature of the ANN loadflow computation is that there is no possibility of non-convergence as it might occur with iterative methods like NRL and SSDL described in “Super Super Decoupled Loadflow, Presented at IEEE International Conference—Science and Technology for Humanity (TIC-STH 2009), pp. 252-259” by Suresh B. Patel. Once an ANN is trained, it gives output in negligible time by simple direct arithmetic operations on a given set of inputs of power system operating condition. The ANN Loadflow can replace the conventional NRL and SSDL methods in real time power system operation where time constraints are very restrictive.
Artificial Neural Networks (ANNs) can be considered as Information processing systems composed of varying number of simple elements called Neurons distributed into layers. Neurons are organized in an input layer, one or more hidden layers, and an output layer. The connections between elements largely determine network function just as in natural biological nervous systems from which ANNs are inspired. ANN is an intelligent technique that mimics the functioning of a human brain, and emulates human intuition of making decisions and drawing conclusions even when presented with complex, noisy, irrelevant and partial information. The structure of an ANN with only one hidden layer is depicted in FIG. 1, which is generic and abstract with learning memorizing and adapting characteristic. The neurons in FIG. 1 are connected to each other by weighted links over which signals can pass. Each neuron receives multiple inputs from other neurons, except the neurons in the input layer, in proportion to their connection weights and then generates a single output in accordance with an activation function. An activation function can be linear or nonlinear depending on application. Sigmoid or Hyperbolic Tangent activation function is generally used for better performance of ANNs in power system applications. The weights of weighted links from a neuron from input to hidden layer is defined as Wih, and the weights of weighted links from a neuron from hidden to output layer is defined as Who. The total number or neurons in input, hidden and output layers are Ik, hk and ok, respectively, where subscript k takes values of 1 to p, q, and r respectively meaning each layer has different number of neurons as shown in FIG. 1. The number of neurons in input layer is the same as number of input variables/parameters, the number of neurons in output layer is the same as number of outputs variables/parameters, and the number of neurons in hidden layer is determined experimentally.
An ANN can be trained to perform a particular function by adjusting values of the interconnections called weights, and neuron thresholds. The process of adjusting interconnection weights and neuron thresholds to achieve output of the ANN the same as the target value or desired output for a given input as depicted in FIG. 2 is called training of ANN. Training or an ANN consists of adjusting interconnection weights of neurons using a learning algorithm. Back propagation with momentum is the commonly used learning algorithm. Multilayer Feed Forward ANNs with Error Back Propagation learning algorithm are commonly used in power system applications. Feed Forward calculations, and propagating error from output layer to input layer and weight updating in hidden and output layers are major steps of training algorithm. ANNs are also sometimes referred to as Neural Networks (NNs). Anybody skilled in the art of the process of training, testing and validating, forming/defining, storing, and then solving prior art or invention based ANN model of a device or a system or the power system knows that the process is carried out using general purpose single/multi processor computing apparatus. A General purpose computing apparatus is a computer that can be used for developing/creating, testing, and running, different types of programs like word, excel, power point, different browser programs like Internet Explorer and Chrome for surfing on Internet (World Wide Web), and even different types of Loadflow Computation Programs, and many other types of programs.
The prior art ANN training process can be divided into four modules. The training, and testing and validating process is carried out off-line, and it is the supervised process.
1. Definition of Input and Output Data Sets/Vectors:                The prior art ANN Loadflow method of “Artificial neural networks for load flow and external equivalents studies, Electric Power Systems Research (2010) article in press” by H. H. Muller, M. J. Rider and C. A. Castro, suggest the input data vector of dimension 2(m+k+1) given below.Gd=Vg2GdNORM−PLNOM+PgpvNORM+CVp  (1)Bd=−Vg2BdNORM−QLNORM+CVq  (2)        Where, GdNORM and BdNORM are the diagonal elements of conductance and susceptance matrices, normalized with respect to the respective largest element in base case. Load powers PLNORM and QLNORM, as well as generation power Pg are also normalized with respect to their base case values. Voltages of generator buses Vg are also included. Contingency information is also added to equations (1) and (2) through CVp and CVq. The authors write, “This additional information was included to compensate the loss of information associated to changes in off-diagonal terms of the admittance matrix.” The definition of equations (1) and (2) is given in the same language of authors.        
2. Training, and Testing and Validating Data Modeling:                The idea of simulating daily load curve is used for generating training, and testing and validating data sets/vectors. Therefore, for each training, and testing and validating demand profile, there is a base case and a set of contingencies, in order to simulate possible cases that could occur in practice. For the training data, the load range is defined as [0.75-1.25]pu. As for testing and validating data, this range is defined as [0.73-1.27]pu, taking into account that the testing and validating data should be different from those of training. These load ranges are applied simultaneously for all buses. For each input data set/vector representing power system operating condition, conventional loadflow computation by method like NRL or SSDL method is performed in off line mode to obtain corresponding output data set/vector. Contingencies that result in islanding, multiple contingencies, voltage magnitudes below 0.75 pu, and angles outside greater and beyond −80° and +80° are not considered for either the training, and testing and validating data sets/vectors.        
3. Run and Error Control:                Each pair of input data set/vector of power system operating condition and corresponding output data set/vector of loadflow computation used as target or desired output is applied to ANN normally simulated on computer. The process of this step requires initialization of minimum number of neurons in hidden layer, and random synaptic weights of interconnections of neurons. Number of neurons in input layer is decided by number of elements of input data set/vector, and number of neurons in output layer is decided by number of elements of output data set/vector. With the initialization number of neurons in hidden layer, random synaptic weights of interconnections and application of input data set/vector, feed-forward action of the ANN generates or calculates its output data set/vector, which is compared against the target data set/vector as in FIG. 2. Error of this comparison is feed back by Back Propagation with momentum using steepest gradient descent technique or second order Levenberg-Marquardt algorithm to update the interconnection weights and threshold of neurons. This process is continued iteratively until error produced is acceptably small for all input/output data sets/vectors generated for training of ANN. Trained ANN is then tested and validated if it has learned to produce accurate enough output data sets/vectors for a given set of input data sets/vectors which are different than those used in training. In testing and validating phase, error in output data set/vector is not feedback to update weights of interconnection of neurons. If the error vector in testing and validating phase is not small enough further training is carried out followed again by testing and validating phase. This process of training followed by testing and validating is iterated until testing and validating phase produce errors acceptably small enough, and the best ANN is stored in terms of values of interconnection weights and number of neurons in different layers for actual use in solving problems for which it is trained. However, for a given set of inputs data sets/vectors the rate of convergence of training, and testing and validating process largely depends upon the number of hidden neurons, learning rate, momentum factor, and the initial values of synaptic weights. Clearly, the proper choice of all these parameters is very difficult and involves too many trials as well as uncertainties leading to several thousands of iterations for the convergence of training, and testing and validating process.        
4. Processing Results:                Stored ANN in terms of values of interconnection weights, number of neurons in different layers and its performance is analyzed and recorded errors are shown and plotted for future reference and possible use.Calculation Steps Prior Art ANNL Method:        
The steps of ANN Loadflow computation method are shown in the flowchart of FIG. 3. Referring to the flowchart of FIG. 3, different steps are elaborated in steps marked with similar letters in the following. The words “Road system data” in Step-a correspond to step-10 and step-20 in FIG. 7, and step-16, step 18, step-24, step-36, step-38 in FIG. 8. All other steps in the following correspond to step-30 in FIG. 7, and step-42, step-44, and step-46 in FIG. 8.    a. Read system data    b. Form nodal admittance matrix    c. Foam input data vector using equation (1) and (2) for stored ANN, which is trained, tested and validated as per modules-1 to 4 in the above.    d. Map (Calculate) high quality and accuracy ANN Loadflow output data set/vector (solution) for a given input data set/vector using stored ANN.    c. If stored ANN trained, and tested and validated using conventional loadflow computation method like NRL or SSDL with control adjustments that accounts for physical limits of power network component equipments like reactive power generation limits of generators, and tap changing limits of tap changing transformers, go to step-g, or else follow the next step-f.    f. Perform conventional loadflow computation using method like NRL or SSDL with control adjustments using high quality initialization loadflow solution yielded by ANN    g. From calculated and known values of voltage magnitude and voltage angle at different power network nodes, and tap position of tap changing transformers, calculate power flows through power network components, and reactive power generation at PV-nodes.